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Step Steady-State Error

An LTI system having transfer function G(s) = 10/(s + 5) is controlled by a proportional controller with a gain of Kp = 2. Consider the unity feedback system. Find the steady state error of the closed loop system, if the reference signal is a step input with a magnitude of 5.

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Answer & Explanation

Correct AnswerA. 1

Quick Explanation

With proportional gain Kp=2, the forward path is 20/(s+5). The position error constant is Kp0=lim GOL(s)=4. For a step of magnitude 5, e_ss=5/(1+4)=1.

Formula / Key Relation

Kp0=limₛ→0 20/(s+5)=4; e_ss=A/(1+Kp0)=5/5=1

Step Steady-State Error explanatory diagram

Detailed Explanation

Correct Answer

A — 1

Concept and Reasoning

With proportional gain Kp=2, the forward path is 20/(s+5). The position error constant is Kp0=lim GOL(s)=4. For a step of magnitude 5, e_ss=5/(1+4)=1.

Calculation / Key Relation

Kp0=limₛ→0 20/(s+5)=4

e_ss=A/(1+Kp0)=5/5=1

Exam Takeaway

For a type-0 unity-feedback system, step error is A/(1+Kp0).

Common Mistake

Do not use the controller gain alone as the position error constant.

Quick Trick

For a type-0 unity-feedback system, step error is A/(1+Kp0).

Common Mistake

Do not use the controller gain alone as the position error constant.

Exam Tip

For a type-0 unity-feedback system, step error is A/(1+Kp0).

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QP-112-202425.pdf2024Q. 18

Step Steady-State Error

Quick Explanation

Formula / Key Relation

Detailed Explanation

Correct Answer

Concept and Reasoning

Calculation / Key Relation

Exam Takeaway

Common Mistake

Quick Trick

Common Mistake

Exam Tip

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